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<li><a class="reference internal" href="#">Multi-class AdaBoosted Decision Trees</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-ensemble-plot-adaboost-multiclass-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="multi-class-adaboosted-decision-trees">
<span id="sphx-glr-auto-examples-ensemble-plot-adaboost-multiclass-py"></span><h1>Multi-class AdaBoosted Decision Trees<a class="headerlink" href="#multi-class-adaboosted-decision-trees" title="Permalink to this headline">¶</a></h1>
<p>This example reproduces Figure 1 of Zhu et al <a class="footnote-reference brackets" href="#id3" id="id1">1</a> and shows how boosting can
improve prediction accuracy on a multi-class problem. The classification
dataset is constructed by taking a ten-dimensional standard normal distribution
and defining three classes separated by nested concentric ten-dimensional
spheres such that roughly equal numbers of samples are in each class (quantiles
of the <span class="math notranslate nohighlight">\(\chi^2\)</span> distribution).</p>
<p>The performance of the SAMME and SAMME.R <a class="footnote-reference brackets" href="#id3" id="id2">1</a> algorithms are compared. SAMME.R
uses the probability estimates to update the additive model, while SAMME  uses
the classifications only. As the example illustrates, the SAMME.R algorithm
typically converges faster than SAMME, achieving a lower test error with fewer
boosting iterations. The error of each algorithm on the test set after each
boosting iteration is shown on the left, the classification error on the test
set of each tree is shown in the middle, and the boost weight of each tree is
shown on the right. All trees have a weight of one in the SAMME.R algorithm and
therefore are not shown.</p>
<dl class="footnote brackets">
<dt class="label" id="id3"><span class="brackets">1</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id2">2</a>)</span></dt>
<dd><ol class="upperalpha simple" start="10">
<li><p>Zhu, H. Zou, S. Rosset, T. Hastie, “Multi-class AdaBoost”, 2009.</p></li>
</ol>
</dd>
</dl>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="c1"># Author: Noel Dawe &lt;noel.dawe@gmail.com&gt;</span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</span>

<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_gaussian_quantiles</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">AdaBoostClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</span>


<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_gaussian_quantiles</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">13000</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
                               <span class="n">n_classes</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

<span class="n">n_split</span> <span class="o">=</span> <span class="mi">3000</span>

<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="n">n_split</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">n_split</span><span class="p">:]</span>
<span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">y</span><span class="p">[:</span><span class="n">n_split</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">n_split</span><span class="p">:]</span>

<span class="n">bdt_real</span> <span class="o">=</span> <span class="n">AdaBoostClassifier</span><span class="p">(</span>
    <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
    <span class="n">n_estimators</span><span class="o">=</span><span class="mi">600</span><span class="p">,</span>
    <span class="n">learning_rate</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

<span class="n">bdt_discrete</span> <span class="o">=</span> <span class="n">AdaBoostClassifier</span><span class="p">(</span>
    <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
    <span class="n">n_estimators</span><span class="o">=</span><span class="mi">600</span><span class="p">,</span>
    <span class="n">learning_rate</span><span class="o">=</span><span class="mf">1.5</span><span class="p">,</span>
    <span class="n">algorithm</span><span class="o">=</span><span class="s2">&quot;SAMME&quot;</span><span class="p">)</span>

<span class="n">bdt_real</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">bdt_discrete</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>

<span class="n">real_test_errors</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">discrete_test_errors</span> <span class="o">=</span> <span class="p">[]</span>

<span class="k">for</span> <span class="n">real_test_predict</span><span class="p">,</span> <span class="n">discrete_train_predict</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span>
        <span class="n">bdt_real</span><span class="o">.</span><span class="n">staged_predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">),</span> <span class="n">bdt_discrete</span><span class="o">.</span><span class="n">staged_predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)):</span>
    <span class="n">real_test_errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
        <span class="mf">1.</span> <span class="o">-</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">real_test_predict</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
    <span class="n">discrete_test_errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
        <span class="mf">1.</span> <span class="o">-</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">discrete_train_predict</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>

<span class="n">n_trees_discrete</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">bdt_discrete</span><span class="p">)</span>
<span class="n">n_trees_real</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">bdt_real</span><span class="p">)</span>

<span class="c1"># Boosting might terminate early, but the following arrays are always</span>
<span class="c1"># n_estimators long. We crop them to the actual number of trees here:</span>
<span class="n">discrete_estimator_errors</span> <span class="o">=</span> <span class="n">bdt_discrete</span><span class="o">.</span><span class="n">estimator_errors_</span><span class="p">[:</span><span class="n">n_trees_discrete</span><span class="p">]</span>
<span class="n">real_estimator_errors</span> <span class="o">=</span> <span class="n">bdt_real</span><span class="o">.</span><span class="n">estimator_errors_</span><span class="p">[:</span><span class="n">n_trees_real</span><span class="p">]</span>
<span class="n">discrete_estimator_weights</span> <span class="o">=</span> <span class="n">bdt_discrete</span><span class="o">.</span><span class="n">estimator_weights_</span><span class="p">[:</span><span class="n">n_trees_discrete</span><span class="p">]</span>

<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">131</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_trees_discrete</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span>
         <span class="n">discrete_test_errors</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;SAMME&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_trees_real</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span>
         <span class="n">real_test_errors</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span>
         <span class="n">linestyle</span><span class="o">=</span><span class="s1">&#39;dashed&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;SAMME.R&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mf">0.18</span><span class="p">,</span> <span class="mf">0.62</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Test Error&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Number of Trees&#39;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">132</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_trees_discrete</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="n">discrete_estimator_errors</span><span class="p">,</span>
         <span class="s2">&quot;b&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;SAMME&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_trees_real</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="n">real_estimator_errors</span><span class="p">,</span>
         <span class="s2">&quot;r&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;SAMME.R&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Error&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Number of Trees&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">((</span><span class="o">.</span><span class="mi">2</span><span class="p">,</span>
         <span class="nb">max</span><span class="p">(</span><span class="n">real_estimator_errors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span>
             <span class="n">discrete_estimator_errors</span><span class="o">.</span><span class="n">max</span><span class="p">())</span> <span class="o">*</span> <span class="mf">1.2</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">((</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">bdt_discrete</span><span class="p">)</span> <span class="o">+</span> <span class="mi">20</span><span class="p">))</span>

<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">133</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_trees_discrete</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="n">discrete_estimator_weights</span><span class="p">,</span>
         <span class="s2">&quot;b&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;SAMME&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Weight&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Number of Trees&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">discrete_estimator_weights</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1.2</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">((</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="n">n_trees_discrete</span> <span class="o">+</span> <span class="mi">20</span><span class="p">))</span>

<span class="c1"># prevent overlapping y-axis labels</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">wspace</span><span class="o">=</span><span class="mf">0.25</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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